Chapter 3.5, Problem 1A

Solution

To state: The coordinates of each corner of your classroom assuming any one corner of your classroom as the origin of a three-dimensional coordinate system like the classroom shown.

The coordinates are:

  $\begin{array}{l}A=\left(0,0,0\right),B=\left(0,0,10\right),C=\left(0,10,10\right),D=\left(0,10,0\right),E=\left(10,0,0\right),F=\left(10,10,0\right),\\ G=\left(10,10,10\right),H=(10,0,10)\end{array}$

Given information:

The given statement says to write the coordinates of each corner of your classroom.

Explanation:

It is known that in a three-dimensional space, the coordinate system is based on the three mutually perpendicular coordinate axes that are x- axis, y- axis, and z- axis.

These three axes intersect at the point known as origin.

Let’s take the length, width, and height of the room is 10ft. each.

Now take any corner of the room as an origin and write the coordinates of each corner.

The coordinates of each corner are:

  $\begin{array}{l}A=\left(0,0,0\right),B=\left(0,0,10\right),C=\left(0,10,10\right),D=\left(0,10,0\right),E=\left(10,0,0\right),F=\left(10,10,0\right),\\ G=\left(10,10,10\right),H=(10,0,10)\end{array}$

The graphical representation of the coordinates is: